Recent content by physicsforum7

Hi. I have one general question and one specific question (which is related by example.) Specific: If I am sitting in a chair with wheels and I push off against a wall, I accelerate. But the force was not applied through any distance. Did I do any work? (I know that an impulse was applied...

My professor gave the "can be put in linear form" definition; hence my confusion. Thank you guys for easing my mind.

Where on Wolfram Alpha are you able to find something that tells you whether a DE is linear or nonlinear?

Homework Statement Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations 1. Homework Statement [/b] Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations \sqrt{xy'+2x2}=5 The Attempt...

Excellent! Thank you very much for your patience and your help.

No, that's not what I'm saying. Rather, given the nonnegative real number 2, 4 is an identity of 2. Because 2*4=2=4*2. But I think I've just discovered my mistake. Let me know if this is right: an identity e is a SINGLE element of a set S for which a*e=e*a=a FOR EVERY a in S. In other...

I hope you'll pardon my slowness; I still don't understand the second paragraph you wrote. When you say, "When you are saying that 2x is the identity of *. What is it that you mean?? What is x? Can we let x take on every real number?? The notation does not make any sense." I am confused...

Aha! But I'm not entirely convinced yet. What of inverses? Isn't -x the inverse of x with respect to addition in the set of real numbers? Surely 2x is as much a number as -x... right?

I was thinking about identities, and seem to have arrived at a contradiction. I'm sure I'm missing something. A(n) (two-sided) identity for a binary operation must be unique. I will reproduce the familiar proof: Proof: Suppose a is an arbitrary element of a set S, e and e' are both...

Homework Statement This problem is from Charles C. Pinter's A Book of Abstract Algebra, Second Edition. The problem is B7 of Chapter 2.Show that the operation * is either associative or not. x*y=\frac{xy}{x+y+1} This problem seems simple to me: I keep arriving at YES for an answer...